# Lesson 3

Interpreting Inequalities

### Problem 1

There is a closed carton of eggs in Mai's refrigerator. The carton contains $$e$$ eggs and it can hold 12 eggs.

1. What does the inequality $$e < 12$$ mean in this context?

2. What does the inequality $$e > 0$$ mean in this context?

3. What are some possible values of $$e$$ that will make both $$e < 12$$ and $$e > 0$$ true?

### Problem 2

Here is a diagram of an unbalanced hanger.

1. Write an inequality to represent the relationship of the weights. Use $$s$$ to represent the weight of the square in grams and $$c$$ to represent the weight of the circle in grams.
2. One red circle weighs 12 grams. Write an inequality to represent the weight of one blue square.
3. Could 0 be a value of $$s$$? Explain your reasoning.

### Problem 3

Here is an inequality: $$\text-3x > 18$$.

1. List some values for $$x$$ that would make this inequality true.
2. How are the solutions to the inequality $$\text-3x \geq 18$$ different from the solutions to $$\text-3x > 18$$? Explain your reasoning.

### Problem 4

Tyler has more than \$10. Elena has more money than Tyler. Mai has more money than Elena. Let $$t$$ be the amount of money that Tyler has, let $$e$$ be the amount of money that Elena has, and let $$m$$ be the amount of money that Mai has. Select all statements that are true:

A:

$$t < j$$

B:

$$m > 10$$

C:

$$e > 10$$

D:

$$t > 10$$

E:

$$e > m$$

F:

$$t < e$$

### Solution

For each inequality, find two values for $$x$$ that make the inequality true and two values that make it false.
1. $$x+3>70$$
2. $$x+3<70$$
3. $$\text-5x<2$$
4. $$5x<2$$